Question

The triangle below is isosceles. Find the length of side & in simplest radical form with

a rational denominator

Answer 1

Answer: x = 10
`√(2)`

Explanation:

We are given that this is an isosceles triangle and the little box represents 90 degrees. This means that both the "legs" of the triangle are equal to 10 and the hypotenuse is equal to x. Since this is a right triangle, we can use the Pythagorean theorem to solve.

a² + b² = x²

10² + 10² = x²

100 + 100 = x²

200 = x²

`√(200)` = x

x =
`√(200)`

x =
`√(2*100)`

x = 10
`√(2)`